If you need a secure login system for your Chrome Extension, but you don't want to or don't know how to create all of the necessary gear--authentication servers, databases...---you can use the oAuth2/OpenID Connect protocols (specifically OpenID Connect) to create one for you.

By delegating the authentication (different from authorization) of your login system to a secure, trusted login system like Google's, you can have a safe and secure system for your Chrome Extension up and running in no time.